*3.2. An Electrical Power Network of the Mining Industry and the Source of the PQ Data*

The PQ data used in the investigation concerns real measurements made in substations of the copper industry's electrical power network. The 110-kV substation of the mining industry works in a four-section system in cooperation with the four transformers (T1, T2, T3, T4). Normally, all the transformers are supplied from a different 110 kV section. However, during the measurements, the T4 transformer was not loaded. Thus:


The presented PQ data concerns four weeks of measurements from 27th of April to 25th of May. The measurements were conducted synchronously with class A PQ recorders [80]. This is more than the classical one week of observation time, and therefore, the PQ data may consist of different working conditions of the analyzed electrical power network of the mining industry [77]. Thus, the different working conditions may be connected to:

MAIN LOADS:


DISTRIBUTED GENERATION:


Thus, the PQ measurements include the analysis of the PQ level, which concerns the impact of the DG and main load (welding machine) on the medium voltage (MV) network. The simplified scheme of the copper industry network, showing the localization of power quality recorders installed in selected bays and the localization of DG, is presented in Figure 2. The PQ recorders involve the measurements of transformers at 6 kV side (T1, T2, T3) and an outcoming feeder to a welding machine (WM).

**Figure 2.** The simplified scheme of the electrical power network of the mining industry containing the placement of the PQ recorder and distributed generation.

It is important to note that the local generation is connected at the 6 kV level and that it consists of heat, a powerplant (G1–10 MW CHP), and steam-gas generation units (G3–15 MW gas unit and G2−13,5 MW steam unit). During the measurements, G1 was out of order and the level of generation of G2 and G3 was changing. The level of DG power (G1, G2, G3) and active power transformers (T1, T2, T3, WM) at the MV level are presented in Figure 3.

**Figure 3.** Active power of the high/medium (HV/MV) transformers T1, T2, and T3, welding machine (WM), and distributed generations G1, G2, G3 using the MV side measurements.

*3.3. Cluster Analysis Results*

## 3.3.1. Parameters Included to the Input Database

For the implementation of hierarchical cluster analysis, the Ward algorithm was used. The reason for this is due to the fact that the data assigned to clusters are characterized by the smallest variation of results (minimum variance of data in clusters). A data set for clustering consisted of the following PQ parameters:


The indicated database consists of parameters, which are considered in the classical PQ assessment in accordance with the standard EN 50160 [81] but were extended to the active power in the measuring points. The noticeable change was the use of short-term flicker severity in place of long-term flicker severity. This change is connected with the time aggregations of the parameters; the long-term severity has 2 h, and the short-term one has 10 min [82,83]. Thus, the application of short term flicker severity enables a database consisting of parameters that are aggregated with 10 min intervals to be built, as is demanded in the standard of International Electrotechnical Commission (IEC) 61000-4-30 [80]. The analyzed measurement data were divided into flagged and unflagged data in accordance with the flagging concept of the standard IEC 61000-4-30 [80]. The data that was input to the CA were free of voltage events.

Additionally, due to the feature of the Ward algorithm that involves the fact that clustering is conducted in order to connect data concentrated in an average value until the data has similar values (range), the standardization process was proposed. The standardization of the parameters aims to obtain unified values by dividing the current value of a particular element of the time series by their maximum values. The decision concerning standardizing data to the average value reduces the problem with regards to different ranges and units of the PQ parameters. The standardize division 0–1 assures the possibility of comparing the changeability of the parameters.
